Edge state, bound state, and anomalous dynamics in the Aubry-André-Harper system coupled to non-Markovian baths
Abstract
In this paper, we study bound states and their influence upon the dynamics of a one-dimensional tight-binding system coupled to an environment. We identify three specific kinds of bound states; the first is a discrete bound state (DBS), for which the energy level exhibits a gap from the continuum. The DBS exhibits similar localization features to the edge states of the system and can therefore suppress its decay. The second is a bound state in the continuum (BIC), which can also suppress system decay. The BIC states are found to be strongly connected to the edge mode of the system, since they both show almost the same localization and energy features. The third bound state displays a large gap from the continuum and exhibits extendible (i.e., not localized) behavior. The population of the system in this state decays partially but not entirely, unlike the other bound states. The time evolution of a single excitation in the system is studied to illustrate the influence of the bound states. We find that both the DBS and the BIC play important roles in time evolution; for example, the excitation becomes localized and does not decay depending on the overlap between the initial state and the DBS or the BIC. Furthermore, we observe that the single excitation can show a long-range hopping in a system when the system falls into the strong localizations regime. This feature can be understood by the interplay of system localizations and the bath-induced long-range correlation.
- Publication:
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Physical Review A
- Pub Date:
- September 2020
- DOI:
- 10.1103/PhysRevA.102.032209
- arXiv:
- arXiv:2004.02201
- Bibcode:
- 2020PhRvA.102c2209C
- Keywords:
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- Quantum Physics
- E-Print:
- 15 pages